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2 years ago

Refer to the attached image

Mathematics

1 answer:

Hatshy [7]2 years ago

6 0

Answer: $\boldsymbol{2(x-2)(5x+7)}$

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Work Shown:

$(4x^2-16)+3(2x-4)(x+1)\\\\4(x^2-4)+3*2(x-2)(x+1)\\\\4(x-2)(x+2)+3*2(x-2)(x+1) \ \text{ ... difference of squares rule}\\\\2*2(x-2)(x+2)+3*2(x-2)(x+1)\\\\2(x-2)(2(x+2)+3(x+1))\\\\2(x-2)(2x+4+3x+3)\\\\\boldsymbol{2(x-2)(5x+7)}\\\\$

The answer has been confirmed with WolframAlpha which is basically a calculator app, but does a ton more than any average calculator.

The CAS (computer algebra system) in the app GeoGebra is another tool I use all the time.

Yet another way to confirm the answer is to graph the original expression and the answer as separate functions. You should find they produce the exact same curve. One curve perfectly overlaps the other. This visually verifies the two expressions are the same thing, just written a different way of course.

Let me know if you have any questions about any step. The basic idea I did was to pull out the GCF and then combine like terms.

You might be interested in

Which one of the following is equivalent to 41/2 = 2?

BARSIC [14]

Answer:

20 $\frac{1}{2}$

Step-by-step explanation:

7 0

4 years ago

Simplify 4z2 + z2 + 6a

Ne4ueva [31]

Answer:

5z^2+6a is the answer I think

3 0

3 years ago

The sum of two consecutive odd integers is 244.what is the smaller integer?

abruzzese [7]

The question gives us that the sum of two consecutive odd integeres is 244, and we are asked to find the value of the smaller integer. Well, we can first assign the variable x to the smaller integer, and the variable y to the larger odd integer.

x = smaller odd integer
y = larger odd integer

The question says that the sum of two consecutive odd integers is 244. This means that if x is an odd integer, the next odd integer can be expressed as x + 2. This means that the value of y is x + 2. Next, we can create an equation modeling the problem.
x + y = 244
x + (x + 2) = 244
x + x + 2 = 244
2x + 2 = 244
2x = 242
x = 121
Therefore, the value of the smaller integer is 121, and the value of the larger integer is 121 + 2 = 123. Hope this helped and have a phenomenal day!

4 0

3 years ago

jolli1 [7]

Answer:

$E = 30 \times H$

$570

Step-by-step explanation:

Given that:

For each hour of tutoring, Lena earns 30 dollars.

E is her earning and

H is the number of hours for which she tutors.

To find:

Equation relating E to H.

Solution:

Let Lena tutors for 1 hour, then the earning = 30 dollars

Let Lena tutors for 2 hours, then the earning = 30+30 OR 2 $\times$ 30 = 60 dollars

Let Lena tutors for 3 hours, then the earning = 30+30 +30 OR 3 $\times$ 30 = 90 dollars

If Lena tutors for H number of hours, then the earning, E = 30 + 30 + .... + 30 (H times) i.e.

$E = 30 \times H$

So, the equation that relates E to H is given as:

$E = 30 \times H$

Now, it is given that she tutors for 19 hours.

Let us put H = 19 hours in the above equation:

$E = 30 \times 19 \\\Rightarrow E = \$570$

Therefore, the earning for 19 hours of tutoring is 570 Dollars.

4 0

4 years ago

Tell whether the ratios form a proportion. 2/5,40/16

lisabon 2012 [21]

Answer:

No, those ratios are not proportional.

Step-by-step explanation:

The reason for them not being proportional is because 2/5 is already in its simplest form and 40/16 in its simplest form is 5/2, resulting in them not being equivalent meaning that they are not proportional.

5 0

3 years ago

Refer to the attached image​

Refer to the attached image